The influence of viscoelasticity on the emptying of liquids from model gravure cells is studied via numerical simulations. The simulations use a finite-element/front-tracking method, and viscoelastic effects are described with the FENE-P model. Two different model configurations featuring moving contact lines are considered. In the first, there is a free surface and an outlet boundary, and the liquid is driven out of a cavity by a combination of horizontal substrate motion and an imposed pressure gradient. In the second, there are two free surfaces, and the liquid is driven out of the cavity through both horizontal and vertical substrate motion. For the first configuration, it is found that viscoelasticity aids cavity emptying through gradients in the first normal stress difference that are generated by the relative motion of the substrate and cavity. For the second configuration, vertical substrate motion promotes cavity emptying, with the effect enhanced when viscoelasticity is present. (C) 2015 Elsevier B.V. All rights reserved.